We propose a simple theory of predatory pricing, based on scale economies and sequential buyers (or markets). The entrant (or prey) needs to reach a critical scale to be successful. The incumbent (or predator) is ready to make losses on earlier buyers so as to deprive the prey of the scale it needs, thus making monopoly profits on later buyers. Several extensions are considered, including markets where scale economies exist because of demand externalities or two-sided market effects, and where markets are characterised by common costs. Conditions under which predation may take place in actual cases are also discussed.